EmoSSR: SSR regular frequency

In this project, we investigated whether the human brain can extract emotional information from a series of faces flickering at specific frequencies.

# setwd(paste0(getwd(), "/SSR/regular_freq")) # set working subdir

filenames <- c( # variable with file names
  # participants x orientation x regularity
  rep(list.files(pattern = ".csv")[1], each = (31 * 2 * 3)), # exp1_hiVar
  rep(list.files(pattern = ".csv")[2], each = (31 * 2 * 3)), # exp1_loVar
  rep(list.files(pattern = ".csv")[3], each = (30 * 2 * 3)), # exp2_hiVar
  rep(list.files(pattern = ".csv")[4], each = (30 * 2 * 3)), # exp2_loVar
  rep(list.files(pattern = ".csv")[5], each = (16 * 2 * 3)), # pilot1
  rep(list.files(pattern = ".csv")[6], each = (16 * 2 * 3)), # pilot2_hiVar
  rep(list.files(pattern = ".csv")[7], each = (16 * 2 * 3)) # pilot2_loVar
)

EmoSSR.data <- list.files(pattern = ".csv") %>% # list of csv files in current directory
  map_df(~ read_csv(.)) %>% # apply read_csv to file list
  mutate(
    filenames = factor(filenames, # add filenames
      levels = c(
        unique(filenames)[5], unique(filenames)[6], unique(filenames)[7], # sort pilots first
        unique(filenames)[1], unique(filenames)[2], unique(filenames)[3], unique(filenames)[4]
      )
    ),
    # create, rename, and recode variables
    experiment = factor(
      case_when(
        grepl("pilot1", filenames) ~ "pilot1",
        grepl("pilot2", filenames) ~ "pilot2",
        grepl("exp1", filenames) ~ "exp1",
        grepl("exp2", filenames) ~ "exp2"
      ),
      levels = c("pilot1", "pilot2", "exp1", "exp2")
    ),
    variability = as.factor(
      case_when(
        grepl("hiVar", filenames) ~ "high",
        grepl("loVar", filenames) ~ "low"
      )
    ),
    participant = as.factor(subj),
    orientation = recode(
      factor(face_dir),
      "1" = "upright", "2" = "inverted"
    ),
    regularity = recode(
      factor(emo),
      "1" = "angry", "2" = "neutral", "3" = "irregular"
    )
  ) %>%
  unite(condition, c(orientation, regularity, variability), sep = "_", remove = FALSE) %>%
  dplyr::select(experiment, participant, orientation, regularity, variability, condition, CS = "data")

We conducted 2 pilots and 2 main experiments.

summary.EmoSSR.data <- summarySEwithin(
  data = EmoSSR.data,
  measurevar = "CS",
  betweenvars = "experiment",
  withinvars = c("orientation", "regularity", "variability"),
  idvar = "participant"
) %>%
  mutate(
    CI.95.low = CS - ci,
    CI.95.high = CS + ci
  ) %>%
  dplyr::select(-c(sd, se, ci))

kable(summary.EmoSSR.data, digits = 2)

experiment	orientation	regularity	variability	N	CS	CI.95.low	CI.95.high
pilot1	upright	angry	NA	16	0.03	0.01	0.04
pilot1	upright	neutral	NA	16	0.05	0.04	0.06
pilot1	upright	irregular	NA	16	0.00	0.00	0.01
pilot1	inverted	angry	NA	16	0.03	0.01	0.04
pilot1	inverted	neutral	NA	16	0.05	0.04	0.06
pilot1	inverted	irregular	NA	16	0.00	-0.01	0.01
pilot2	upright	angry	high	16	0.06	0.02	0.09
pilot2	upright	angry	low	16	0.02	0.00	0.04
pilot2	upright	neutral	high	16	0.09	0.06	0.12
pilot2	upright	neutral	low	16	0.04	0.03	0.05
pilot2	upright	irregular	high	16	-0.02	-0.04	-0.01
pilot2	upright	irregular	low	16	-0.02	-0.03	-0.01
pilot2	inverted	angry	high	16	0.03	0.02	0.04
pilot2	inverted	angry	low	16	0.03	0.01	0.05
pilot2	inverted	neutral	high	16	0.09	0.06	0.12
pilot2	inverted	neutral	low	16	0.03	0.01	0.05
pilot2	inverted	irregular	high	16	-0.01	-0.02	0.00
pilot2	inverted	irregular	low	16	-0.03	-0.04	-0.01
exp1	upright	angry	high	31	0.04	0.03	0.05
exp1	upright	angry	low	31	0.03	0.02	0.04
exp1	upright	neutral	high	31	0.06	0.04	0.07
exp1	upright	neutral	low	31	0.04	0.02	0.05
exp1	upright	irregular	high	31	0.01	0.00	0.02
exp1	upright	irregular	low	31	0.01	0.00	0.02
exp1	inverted	angry	high	31	0.03	0.02	0.04
exp1	inverted	angry	low	31	0.02	0.01	0.03
exp1	inverted	neutral	high	31	0.04	0.03	0.05
exp1	inverted	neutral	low	31	0.03	0.02	0.04
exp1	inverted	irregular	high	31	0.00	0.00	0.01
exp1	inverted	irregular	low	31	0.00	0.00	0.01
exp2	upright	angry	high	30	0.04	0.03	0.05
exp2	upright	angry	low	30	0.02	0.01	0.03
exp2	upright	neutral	high	30	0.06	0.05	0.08
exp2	upright	neutral	low	30	0.03	0.02	0.04
exp2	upright	irregular	high	30	0.00	0.00	0.01
exp2	upright	irregular	low	30	0.01	0.00	0.02
exp2	inverted	angry	high	30	0.04	0.02	0.05
exp2	inverted	angry	low	30	0.02	0.01	0.02
exp2	inverted	neutral	high	30	0.05	0.04	0.06
exp2	inverted	neutral	low	30	0.02	0.01	0.03
exp2	inverted	irregular	high	30	0.01	0.00	0.01
exp2	inverted	irregular	low	30	0.00	0.00	0.01

EmoSSR.data <- EmoSSR.data %>%
  unite("cond4plot", c(orientation, regularity), sep = " ", remove = FALSE) %>%
  mutate(cond4plot = factor(cond4plot,
    levels = c(
      "upright angry", "upright neutral", "upright irregular",
      "inverted angry", "inverted neutral", "inverted irregular"
    )
  ))

# pilot1 does not have the column "variability", which messes up all the other plots...
# that's why they are created separately instead of calling facet_wrap(~ experiment, scales = "free")

# pilot1
EmoSSR.plot.pilot1 <-
  EmoSSR.data %>%
  filter(experiment == "pilot1") %>%
  ggplot(aes(
    x = cond4plot,
    y = CS,
    color = cond4plot,
    fill = cond4plot
  )) +
  geom_pirate(
    bars = FALSE,
    cis = TRUE,
    lines = TRUE, lines_params = list(color = "black"),
    points = TRUE, points_params = list(shape = 16, color = "black", size = 5, alpha = .2),
    violins = TRUE, violins_params = list(size = 1),
    show.legend = FALSE
  ) +
  scale_y_continuous(
    limits = c(-.1, 1),
    breaks = seq(0, 1, .1)
  ) +
  coord_cartesian(ylim = c(-.06, .4)) +
  geom_hline(
    yintercept = seq(0, 1, .1),
    linetype = "dotted",
    colour = "#999999",
    size = .8,
    alpha = .5
  ) +
  labs(
    x = "",
    y = "CS"
  ) +
  ggtitle("pilot 1") +
  theme_EmoSSR

# pilot2
EmoSSR.plot.pilot2 <-
  EmoSSR.data %>%
  filter(experiment == "pilot2") %>%
  ggplot(aes(
    x = cond4plot,
    y = CS,
    color = variability,
    fill = variability
  )) +
  geom_pirate(
    bars = FALSE,
    cis = TRUE,
    lines = TRUE, lines_params = list(color = "black"),
    points = TRUE, points_params = list(shape = 16, size = 5, alpha = .2),
    violins = TRUE, violins_params = list(size = 1),
    show.legend = TRUE
  ) +
  scale_fill_viridis_d(option = "cividis") +
  scale_color_viridis_d(option = "cividis") +
  scale_y_continuous(
    limits = c(-.1, 1),
    breaks = seq(0, 1, .1)
  ) +
  coord_cartesian(ylim = c(-.06, .4)) +
  geom_hline(
    yintercept = seq(0, 1, .1),
    linetype = "dotted",
    colour = "#999999",
    size = .8,
    alpha = .5
  ) +
  labs(
    x = "",
    y = "CS"
  ) +
  ggtitle("pilot 2") +
  theme_EmoSSR +
  theme(legend.position = c(.8, .8))

# exp1
EmoSSR.plot.exp1 <-
  EmoSSR.data %>%
  filter(experiment == "exp1") %>%
  ggplot(aes(
    x = cond4plot,
    y = CS,
    color = variability,
    fill = variability
  )) +
  geom_pirate(
    bars = FALSE,
    cis = TRUE,
    lines = TRUE, lines_params = list(color = "black"),
    points = TRUE, points_params = list(shape = 16, size = 5, alpha = .2),
    violins = TRUE, violins_params = list(size = 1),
    show.legend = TRUE
  ) +
  scale_fill_viridis_d(option = "cividis") +
  scale_color_viridis_d(option = "cividis") +
  scale_y_continuous(
    limits = c(-.1, 1),
    breaks = seq(0, 1, .1)
  ) +
  coord_cartesian(ylim = c(-.06, .4)) +
  geom_hline(
    yintercept = seq(0, 1, .1),
    linetype = "dotted",
    colour = "#999999",
    size = .8,
    alpha = .5
  ) +
  labs(
    x = "",
    y = "CS"
  ) +
  ggtitle("experiment 1") +
  theme_EmoSSR +
  theme(legend.position = c(.8, .8))

# exp2
EmoSSR.plot.exp2 <-
  EmoSSR.data %>%
  filter(experiment == "exp2") %>%
  ggplot(aes(
    x = cond4plot,
    y = CS,
    color = variability,
    fill = variability
  )) +
  geom_pirate(
    bars = FALSE,
    cis = TRUE,
    lines = TRUE, lines_params = list(color = "black"),
    points = TRUE, points_params = list(shape = 16, size = 5, alpha = .2),
    violins = TRUE, violins_params = list(size = 1),
    show.legend = TRUE
  ) +
  scale_fill_viridis_d(option = "cividis") +
  scale_color_viridis_d(option = "cividis") +
  scale_y_continuous(
    limits = c(-.1, 1),
    breaks = seq(0, 1, .1)
  ) +
  coord_cartesian(ylim = c(-.06, .4)) +
  geom_hline(
    yintercept = seq(0, 1, .1),
    linetype = "dotted",
    colour = "#999999",
    size = .8,
    alpha = .5
  ) +
  labs(
    x = "",
    y = "CS"
  ) +
  ggtitle("experiment 2") +
  theme_EmoSSR +
  theme(legend.position = c(.8, .8))

plot_grid(EmoSSR.plot.pilot1, EmoSSR.plot.pilot2, EmoSSR.plot.exp1, EmoSSR.plot.exp2)

# ### save plots to file
# # pilot1
# file.EmoSSR.plot.pilot1 <- EmoSSR.plot.pilot1 +
#     coord_cartesian(ylim = c(-.06, .12))
# 
# save_plot(paste0(getwd(), "/pilot1_regularFreq.svg"),
#           file.EmoSSR.plot.pilot1,
#           base_aspect_ratio = 1,
#           base_width = 11
#           )
# 
# # pilot2
# save_plot(paste0(getwd(), "/pilot2_regularFreq.svg"),
#           EmoSSR.plot.pilot2,
#           base_aspect_ratio = 1,
#           base_width = 11
#           )
# 
# # exp1
# file.EmoSSR.plot.exp1 <- EmoSSR.plot.exp1 +
#     coord_cartesian(ylim = c(-.06, .23))
# 
# save_plot(paste0(getwd(), "/exp1_regularFreq.svg"),
#           file.EmoSSR.plot.exp1,
#           base_aspect_ratio = 1,
#           base_width = 11
#           )
# 
# # exp2
# file.EmoSSR.plot.exp2 <- EmoSSR.plot.exp2 +
#     coord_cartesian(ylim = c(-.06, .2))
# 
# save_plot(paste0(getwd(), "/exp2_regularFreq.svg"),
#           file.EmoSSR.plot.exp2,
#           base_aspect_ratio = 1,
#           base_width = 11
#           )

For the statistical analyses, we fit Bayesian multilevel models using brms. The constant effect was condition. Intercepts and slopes were allowed to vary as a function of participant.

Pilot 1

• flickering frequency: 15 Hz
• regularity: 5 Hz
• 9 face identities
• task: detect dots on faces

# subset data
EmoSSR.pilot1 <- EmoSSR.data %>%
  filter(experiment == "pilot1") %>%
  dplyr::select(-variability) %>%
  droplevels() %>%
  mutate(condition = as.factor(gsub("_NA", "", condition)))

pilot1.model <- brm(CS ~ 0 + condition # constant effects
+ (0 + condition | participant), # varying effects
data = EmoSSR.pilot1, # subset data current experiment
family = gaussian(), # likelihood function
prior = weak.priors, # priors
sample_prior = TRUE, # draw samples from the prior distribution
inits = "random", # initial parameter values in the chains
control = list(
  adapt_delta = .99, # parameters of NUTS sampler
  max_treedepth = 15
),
chains = num.chains, # number of chains
iter = num.iter, # number of iterations
warmup = num.warmup, # number of warm-up samples
thin = num.thin, # thinning rate
algorithm = "sampling", # type of sampling algorithm
cores = num.chains, # number of processor cores to use when running chains in parallel
seed = seed.smorfia # RNG seed
)

saveRDS(pilot1.model, file = "pilot1_model.rds", compress = "gzip") # save results

# subset data
EmoSSR.pilot1 <- EmoSSR.data %>%
  filter(experiment == "pilot1") %>%
  dplyr::select(-variability) %>%
  droplevels() %>%
  mutate(condition = as.factor(gsub("_NA", "", condition)))

# load model
pilot1.model <- readRDS("pilot1_model.rds")

# summary posterior distributions & diagnostics
summary.pilot1.model <-
  describe_posterior(pilot1.model,
    centrality = "mean",
    ci = 0.95,
    ci_method = "hdi",
    test = NULL,
    diagnostic = "all"
  ) %>%
  mutate(
    Parameter = gsub("b_condition", "", Parameter),
    Parameter2 = gsub("_", " ", Parameter),
    condition = factor(Parameter2,
      levels =
        c(
          "upright angry", "upright neutral", "upright irregular",
          "inverted angry", "inverted neutral", "inverted irregular"
        )
    )
  ) %>%
  dplyr::select(Parameter, Mean, HDI95_Low = CI_low, HDI95_High = CI_high, Estimated_Sample_Size = ESS, MonteCarlo_StdErr = MCSE)

kable(summary.pilot1.model, digits = 2)

Parameter	Mean	HDI95_Low	HDI95_High	Estimated_Sample_Size	MonteCarlo_StdErr
inverted_angry	0.03	0.01	0.05	5713	0
inverted_irregular	0.00	0.00	0.00	14452	0
inverted_neutral	0.05	0.04	0.06	12170	0
upright_angry	0.03	0.01	0.04	13492	0
upright_irregular	0.00	0.00	0.01	14595	0
upright_neutral	0.05	0.04	0.07	13834	0

# MCMC chains
pilot1.model %>%
  spread_draws(`b_.*`, regex = TRUE) %>%
  dplyr::select(
    "Chain" = ".chain",
    "upright angry" = "b_conditionupright_angry",
    "upright neutral" = "b_conditionupright_neutral",
    "upright irregular" = "b_conditionupright_irregular",
    "inverted angry" = "b_conditioninverted_angry",
    "inverted neutral" = "b_conditioninverted_neutral",
    "inverted irregular" = "b_conditioninverted_irregular"
  ) %>%
  as.data.frame() %>%
  mcmc_trace(facet_args = list(ncol = 3)) +
  geom_vline(
    xintercept = seq(0, 2000, 500),
    linetype = "dotted",
    colour = "#999999",
    size = .8,
    alpha = .5
  ) +
  ggtitle("chain convergence") +
  theme_EmoSSR +
  theme(legend.position = "none")

# posterior predictive checks
pilot1.model %>%
  posterior_predict(draws = 500) %>%
  ppc_stat_grouped(
    y = pull(EmoSSR.pilot1, CS),
    group = pull(EmoSSR.pilot1, cond4plot),
    stat = "mean"
  ) +
  ggtitle("posterior predictive checks") +
  theme_EmoSSR +
  theme(legend.position = "none")

pilot1.posterior.test <- pilot1.model %>%
  spread_draws(`b_.*`, regex = TRUE) %>%
  dplyr::select(
    "upright angry" = "b_conditionupright_angry",
    "upright neutral" = "b_conditionupright_neutral",
    "upright irregular" = "b_conditionupright_irregular",
    "inverted angry" = "b_conditioninverted_angry",
    "inverted neutral" = "b_conditioninverted_neutral",
    "inverted irregular" = "b_conditioninverted_irregular"
  ) %>%
  mutate(
    ### orientation
    # angry
    diff.angry.uprightVSinverted = `upright angry` - `inverted angry`,
    # neutral
    diff.neutral.uprightVSinverted = `upright neutral` - `inverted neutral`,
    # irregular
    diff.irregular.uprightVSinverted = `upright irregular` - `inverted irregular`,
    ### regularity
    ## upright
    # angry minus neutral
    diff.upright.angryVSneutral = `upright angry` - `upright neutral`,
    # angry minus irregular
    diff.upright.angryVSirregular = `upright angry` - `upright irregular`,
    # neutral minus irregular
    diff.upright.neutralVSirregular = `upright neutral` - `upright irregular`,
    ## inverted
    # angry minus neutral
    diff.inverted.angryVSneutral = `inverted angry` - `inverted neutral`,
    # angry minus irregular
    diff.inverted.angryVSirregular = `inverted angry` - `inverted irregular`,
    # neutral minus irregular
    diff.inverted.neutralVSirregular = `inverted neutral` - `inverted irregular`
  ) %>%
  gather(key = "condition", value = "CS") %>%
  mutate(condition = factor(condition,
    levels = c(
      "upright angry", "upright neutral", "upright irregular",
      "inverted angry", "inverted neutral", "inverted irregular",
      "diff.angry.uprightVSinverted",
      "diff.neutral.uprightVSinverted",
      "diff.irregular.uprightVSinverted",
      "diff.upright.angryVSneutral",
      "diff.upright.angryVSirregular",
      "diff.upright.neutralVSirregular",
      "diff.inverted.angryVSneutral",
      "diff.inverted.angryVSirregular",
      "diff.inverted.neutralVSirregular"
    )
  ))

# summary
summary.pilot1.posterior.test <- pilot1.posterior.test %>%
  group_by(condition) %>%
  dplyr::summarize(
    mean = mean(CS),
    hdi.95.low = hdi(CS)[1],
    hdi.95.high = hdi(CS)[2],
    evidence.ratio = ifelse(mean < 0,
      length(which(CS < 0)) / length(which(CS > 0)),
      length(which(CS > 0)) / length(which(CS < 0))
    )
  ) %>%
  ungroup()

kable(summary.pilot1.posterior.test, digits = 2)

condition	mean	hdi.95.low	hdi.95.high	evidence.ratio
upright angry	0.03	0.01	0.04	665.67
upright neutral	0.05	0.04	0.07	Inf
upright irregular	0.00	0.00	0.01	319.00
inverted angry	0.03	0.01	0.05	1599.00
inverted neutral	0.05	0.04	0.06	Inf
inverted irregular	0.00	0.00	0.00	1.35
diff.angry.uprightVSinverted	0.00	-0.02	0.02	1.38
diff.neutral.uprightVSinverted	0.01	-0.01	0.02	3.39
diff.irregular.uprightVSinverted	0.00	0.00	0.01	26.49
diff.upright.angryVSneutral	-0.03	-0.05	-0.01	162.27
diff.upright.angryVSirregular	0.02	0.01	0.04	234.29
diff.upright.neutralVSirregular	0.05	0.04	0.06	Inf
diff.inverted.angryVSneutral	-0.02	-0.04	0.00	25.02
diff.inverted.angryVSirregular	0.03	0.01	0.04	1141.86
diff.inverted.neutralVSirregular	0.05	0.03	0.06	Inf

### CSs higher than noise? ###
pilot1.posterior.test.VS.0 <- filter(
  pilot1.posterior.test,
  condition == c(
    "upright angry", "upright neutral", "upright irregular",
    "inverted angry", "inverted neutral", "inverted irregular"
  )
) %>%
  droplevels()

par(mfrow = c(2, 3))

for (i in 1:length(levels(pilot1.posterior.test.VS.0$condition))) {
  temp.data <- filter(pilot1.posterior.test.VS.0, condition == levels(condition)[i])

  plotPost(
    pull(temp.data, CS),
    credMass = 0.95,
    compVal = 0,
    ROPE = NULL,
    xlab = "",
    col = "#b3cde0",
    showCurve = FALSE,
    cex = 1,
    main = levels(temp.data$condition)[i]
  )
}

### Paired comparisons ###
pilot1.posterior.test.paired <- filter(
  pilot1.posterior.test,
  condition == c(
    "diff.angry.uprightVSinverted",
    "diff.neutral.uprightVSinverted",
    "diff.irregular.uprightVSinverted",
    "diff.upright.angryVSneutral",
    "diff.upright.angryVSirregular",
    "diff.upright.neutralVSirregular",
    "diff.inverted.angryVSneutral",
    "diff.inverted.angryVSirregular",
    "diff.inverted.neutralVSirregular"
  )
) %>%
  droplevels()

par(mfrow = c(3, 3))

for (i in 1:length(levels(pilot1.posterior.test.paired$condition))) {
  temp.data <- filter(pilot1.posterior.test.paired, condition == levels(condition)[i])

  plotPost(
    pull(temp.data, CS),
    credMass = 0.95,
    compVal = 0,
    ROPE = NULL,
    xlab = "",
    col = "#b3cde0",
    showCurve = FALSE,
    cex = 1,
    main = levels(temp.data$condition)[i]
  )
}

Take-home messages:

• comparison with 0
  • regular angry and neutral faces elicit SSR reliably larger than noise, in both orientations
  • irregular faces elicit SSR reliably larger than noise only when upright
• paired comparisons:
  • orientation
    • regular angry and neutral faces elicit similar SSR when upright or inverted
    • irregular faces elicit larger SSR when upright compared to inverted
  • regularity
    • regular angry and neutral faces elicit larger SSR compared to irregular faces, in both orientations
    • regular angry faces elicit lower SSR compared to regular neutral faces, in both orientations

---

---

Pilot 2

• flickering frequency: 15 Hz
• regularity: 5 Hz
• 2 face identities
• task: detect dots on faces

# subset data
EmoSSR.pilot2 <- EmoSSR.data %>%
  filter(experiment == "pilot2")

pilot2.model <- brm(CS ~ 0 + condition # constant effects
+ (0 + condition | participant), # varying effects
data = EmoSSR.pilot2, # subset data current experiment
family = gaussian(), # likelihood function
prior = weak.priors, # priors
sample_prior = TRUE, # draw samples from the prior distribution
inits = "random", # initial parameter values in the chains
control = list(
  adapt_delta = .99, # parameters of NUTS sampler
  max_treedepth = 15
),
chains = num.chains, # number of chains
iter = num.iter, # number of iterations
warmup = num.warmup, # number of warm-up samples
thin = num.thin, # thinning rate
algorithm = "sampling", # type of sampling algorithm
cores = num.chains, # number of processor cores to use when running chains in parallel
seed = seed.smorfia # RNG seed
)

saveRDS(pilot2.model, file = "pilot2_model.rds", compress = "gzip") # save results

# subset data
EmoSSR.pilot2 <- EmoSSR.data %>%
  filter(experiment == "pilot2")

# load model
pilot2.model <- readRDS("pilot2_model.rds")

# summary posterior distributions & diagnostics
summary.pilot2.model <-
  describe_posterior(pilot2.model,
    centrality = "mean",
    ci = 0.95,
    ci_method = "hdi",
    test = NULL,
    diagnostic = "all"
  ) %>%
  mutate(
    Parameter = gsub("b_condition", "", Parameter),
    Parameter2 = gsub("_", " ", Parameter),
    condition = factor(Parameter2,
      levels =
        c(
          "upright angry high", "upright neutral high", "upright irregular high",
          "upright angry low", "upright neutral low", "upright irregular low",
          "inverted angry high", "inverted neutral high", "inverted irregular high",
          "inverted angry low", "inverted neutral low", "inverted irregular low"
        )
    )
  ) %>%
  dplyr::select(Parameter, Mean, HDI95_Low = CI_low, HDI95_High = CI_high, Estimated_Sample_Size = ESS, MonteCarlo_StdErr = MCSE)

kable(summary.pilot2.model, digits = 2)

Parameter	Mean	HDI95_Low	HDI95_High	Estimated_Sample_Size	MonteCarlo_StdErr
inverted_angry_high	0.05	0.03	0.07	8437	0
inverted_angry_low	0.05	0.03	0.07	8538	0
inverted_irregular_high	0.01	0.00	0.02	12441	0
inverted_irregular_high	0.01	0.00	0.02	12441	0
inverted_irregular_low	-0.01	-0.01	0.00	13497	0
inverted_irregular_low	-0.01	-0.01	0.00	13497	0
inverted_neutral_high	0.11	0.07	0.14	10957	0
inverted_neutral_low	0.05	0.02	0.08	12095	0
upright_angry_high	0.08	0.04	0.12	11431	0
upright_angry_low	0.04	0.02	0.07	12154	0
upright_irregular_high	0.00	-0.01	0.00	12872	0
upright_irregular_high	0.00	-0.01	0.00	12872	0
upright_irregular_low	0.00	-0.01	0.01	14103	0
upright_irregular_low	0.00	-0.01	0.01	14103	0
upright_neutral_high	0.11	0.07	0.15	12653	0
upright_neutral_low	0.06	0.04	0.08	12522	0

# MCMC chains
pilot2.model %>%
  spread_draws(`b_.*`, regex = TRUE) %>%
  dplyr::select(
    "Chain" = ".chain",
    "upright angry high" = "b_conditionupright_angry_high",
    "upright neutral high" = "b_conditionupright_neutral_high",
    "upright irregular high" = "b_conditionupright_irregular_high",
    "upright angry low" = "b_conditionupright_angry_low",
    "upright neutral low" = "b_conditionupright_neutral_low",
    "upright irregular low" = "b_conditionupright_irregular_low",
    "inverted angry high" = "b_conditioninverted_angry_high",
    "inverted neutral high" = "b_conditioninverted_neutral_high",
    "inverted irregular high" = "b_conditioninverted_irregular_high",
    "inverted angry low" = "b_conditioninverted_angry_low",
    "inverted neutral low" = "b_conditioninverted_neutral_low",
    "inverted irregular low" = "b_conditioninverted_irregular_low"
  ) %>%
  as.data.frame() %>%
  mcmc_trace(facet_args = list(ncol = 3)) +
  geom_vline(
    xintercept = seq(0, 2000, 500),
    linetype = "dotted",
    colour = "#999999",
    size = .8,
    alpha = .5
  ) +
  ggtitle("chain convergence") +
  theme_EmoSSR +
  theme(legend.position = "none")

# posterior predictive checks
pilot2.model %>%
  posterior_predict(draws = 500) %>%
  ppc_stat_grouped(
    y = pull(EmoSSR.pilot2, CS),
    group = pull(EmoSSR.pilot2, condition),
    stat = "mean"
  ) +
  ggtitle("posterior predictive checks") +
  theme_EmoSSR +
  theme(legend.position = "none")

pilot2.posterior.test <- pilot2.model %>%
  spread_draws(`b_.*`, regex = TRUE) %>%
  dplyr::select(
    "upright angry high" = "b_conditionupright_angry_high",
    "upright neutral high" = "b_conditionupright_neutral_high",
    "upright irregular high" = "b_conditionupright_irregular_high",
    "upright angry low" = "b_conditionupright_angry_low",
    "upright neutral low" = "b_conditionupright_neutral_low",
    "upright irregular low" = "b_conditionupright_irregular_low",
    "inverted angry high" = "b_conditioninverted_angry_high",
    "inverted neutral high" = "b_conditioninverted_neutral_high",
    "inverted irregular high" = "b_conditioninverted_irregular_high",
    "inverted angry low" = "b_conditioninverted_angry_low",
    "inverted neutral low" = "b_conditioninverted_neutral_low",
    "inverted irregular low" = "b_conditioninverted_irregular_low"
  ) %>%
  mutate(
    ### orientation
    # angry high
    diff.high.angry.uprightVSinverted = `upright angry high` - `inverted angry high`,
    # neutral high
    diff.high.neutral.uprightVSinverted = `upright neutral high` - `inverted neutral high`,
    # irregular high
    diff.high.irregular.uprightVSinverted = `upright irregular high` - `inverted irregular high`,
    # angry low
    diff.low.angry.uprightVSinverted = `upright angry low` - `inverted angry low`,
    # neutral high
    diff.low.neutral.uprightVSinverted = `upright neutral low` - `inverted neutral low`,
    # irregular high
    diff.low.irregular.uprightVSinverted = `upright irregular low` - `inverted irregular low`,
    ### regularity
    ## upright high
    # angry minus neutral
    diff.high.upright.angryVSneutral = `upright angry high` - `upright neutral high`,
    # angry minus irregular
    diff.high.upright.angryVSirregular = `upright angry high` - `upright irregular high`,
    # neutral minus irregular
    diff.high.upright.neutralVSirregular = `upright neutral high` - `upright irregular high`,
    ## upright low
    # angry minus neutral
    diff.low.upright.angryVSneutral = `upright angry low` - `upright neutral low`,
    # angry minus irregular
    diff.low.upright.angryVSirregular = `upright angry low` - `upright irregular low`,
    # neutral minus irregular
    diff.low.upright.neutralVSirregular = `upright neutral low` - `upright irregular low`,
    ## inverted high
    # angry minus neutral
    diff.high.inverted.angryVSneutral = `inverted angry high` - `inverted neutral high`,
    # angry minus irregular
    diff.high.inverted.angryVSirregular = `inverted angry high` - `inverted irregular high`,
    # neutral minus irregular
    diff.high.inverted.neutralVSirregular = `inverted neutral high` - `inverted irregular high`,
    ## inverted low
    # angry minus neutral
    diff.low.inverted.angryVSneutral = `inverted angry low` - `inverted neutral low`,
    # angry minus irregular
    diff.low.inverted.angryVSirregular = `inverted angry low` - `inverted irregular low`,
    # neutral minus irregular
    diff.low.inverted.neutralVSirregular = `inverted neutral low` - `inverted irregular low`,
    ### variability
    ## upright angry
    diff.upright.angry.highVSlow = `upright angry high` - `upright angry low`,
    ## upright neutral
    diff.upright.neutral.highVSlow = `upright neutral high` - `upright neutral low`,
    ## upright irregular
    diff.upright.irregular.highVSlow = `upright irregular high` - `upright irregular low`,
    ## inverted angry
    diff.inverted.angry.highVSlow = `inverted angry high` - `inverted angry low`,
    ## inverted neutral
    diff.inverted.neutral.highVSlow = `inverted neutral high` - `inverted neutral low`,
    ## inverted irregular
    diff.inverted.irregular.highVSlow = `inverted irregular high` - `inverted irregular low`
  ) %>%
  gather(key = "condition", value = "CS") %>%
  mutate(condition = factor(condition,
    levels = c(
      "upright angry high", "upright neutral high", "upright irregular high",
      "upright angry low", "upright neutral low", "upright irregular low",
      "inverted angry high", "inverted neutral high", "inverted irregular high",
      "inverted angry low", "inverted neutral low", "inverted irregular low",
      "diff.high.angry.uprightVSinverted",
      "diff.high.neutral.uprightVSinverted",
      "diff.high.irregular.uprightVSinverted",
      "diff.low.angry.uprightVSinverted",
      "diff.low.neutral.uprightVSinverted",
      "diff.low.irregular.uprightVSinverted",
      "diff.high.upright.angryVSneutral",
      "diff.high.upright.angryVSirregular",
      "diff.high.upright.neutralVSirregular",
      "diff.low.upright.angryVSneutral",
      "diff.low.upright.angryVSirregular",
      "diff.low.upright.neutralVSirregular",
      "diff.high.inverted.angryVSneutral",
      "diff.high.inverted.angryVSirregular",
      "diff.high.inverted.neutralVSirregular",
      "diff.low.inverted.angryVSneutral",
      "diff.low.inverted.angryVSirregular",
      "diff.low.inverted.neutralVSirregular",
      "diff.upright.angry.highVSlow",
      "diff.upright.neutral.highVSlow",
      "diff.upright.irregular.highVSlow",
      "diff.inverted.angry.highVSlow",
      "diff.inverted.neutral.highVSlow",
      "diff.inverted.irregular.highVSlow"
    )
  ))

# summary
summary.pilot2.posterior.test <- pilot2.posterior.test %>%
  group_by(condition) %>%
  dplyr::summarize(
    mean = mean(CS),
    hdi.95.low = hdi(CS)[1],
    hdi.95.high = hdi(CS)[2],
    evidence.ratio = ifelse(mean < 0,
      length(which(CS < 0)) / length(which(CS > 0)),
      length(which(CS > 0)) / length(which(CS < 0))
    )
  ) %>%
  ungroup()

kable(summary.pilot2.posterior.test, digits = 2)

condition	mean	hdi.95.low	hdi.95.high	evidence.ratio
upright angry high	0.08	0.04	0.12	1453.55
upright neutral high	0.11	0.07	0.15	Inf
upright irregular high	0.00	-0.01	0.00	4.04
upright angry low	0.04	0.02	0.07	1776.78
upright neutral low	0.06	0.04	0.08	Inf
upright irregular low	0.00	-0.01	0.01	1.21
inverted angry high	0.05	0.03	0.07	Inf
inverted neutral high	0.11	0.07	0.14	Inf
inverted irregular high	0.01	0.00	0.02	20.86
inverted angry low	0.05	0.03	0.07	3999.00
inverted neutral low	0.05	0.02	0.08	1141.86
inverted irregular low	-0.01	-0.01	0.00	12.79
diff.high.angry.uprightVSinverted	0.03	-0.02	0.07	8.91
diff.high.neutral.uprightVSinverted	0.00	-0.06	0.06	1.03
diff.high.irregular.uprightVSinverted	-0.01	-0.03	0.00	39.00
diff.low.angry.uprightVSinverted	-0.01	-0.04	0.02	2.54
diff.low.neutral.uprightVSinverted	0.01	-0.01	0.04	4.52
diff.low.irregular.uprightVSinverted	0.00	-0.01	0.02	3.86
diff.high.upright.angryVSneutral	-0.03	-0.08	0.02	9.09
diff.high.upright.angryVSirregular	0.08	0.04	0.12	1776.78
diff.high.upright.neutralVSirregular	0.11	0.07	0.15	Inf
diff.low.upright.angryVSneutral	-0.02	-0.04	0.01	8.19
diff.low.upright.angryVSirregular	0.04	0.02	0.07	1999.00
diff.low.upright.neutralVSirregular	0.06	0.04	0.08	Inf
diff.high.inverted.angryVSneutral	-0.06	-0.09	-0.02	614.38
diff.high.inverted.angryVSirregular	0.04	0.02	0.06	1332.33
diff.high.inverted.neutralVSirregular	0.10	0.06	0.13	Inf
diff.low.inverted.angryVSneutral	0.00	-0.03	0.04	1.29
diff.low.inverted.angryVSirregular	0.06	0.03	0.08	15999.00
diff.low.inverted.neutralVSirregular	0.05	0.03	0.08	1776.78
diff.upright.angry.highVSlow	0.04	-0.01	0.08	12.69
diff.upright.neutral.highVSlow	0.05	0.01	0.09	90.95
diff.upright.irregular.highVSlow	0.00	-0.01	0.01	2.10
diff.inverted.angry.highVSlow	0.00	-0.03	0.03	1.09
diff.inverted.neutral.highVSlow	0.06	0.02	0.10	409.26
diff.inverted.irregular.highVSlow	0.02	0.00	0.03	49.00

### CSs higher than noise? ###
pilot2.posterior.test.VS.0 <- filter(
  pilot2.posterior.test,
  condition == c(
    "upright angry high", "upright neutral high", "upright irregular high",
    "upright angry low", "upright neutral low", "upright irregular low",
    "inverted angry high", "inverted neutral high", "inverted irregular high",
    "inverted angry low", "inverted neutral low", "inverted irregular low"
  )
) %>%
  droplevels()

par(mfrow = c(2, 3))

for (i in 1:length(levels(pilot2.posterior.test.VS.0$condition))) {
  temp.data <- filter(pilot2.posterior.test.VS.0, condition == levels(condition)[i])

  plotPost(
    pull(temp.data, CS),
    credMass = 0.95,
    compVal = 0,
    ROPE = NULL,
    xlab = "",
    col = "#b3cde0",
    showCurve = FALSE,
    cex = 1,
    main = levels(temp.data$condition)[i]
  )
}

### Paired comparisons ###

### orientation
pilot2.posterior.test.orientation <- filter(
  pilot2.posterior.test,
  condition == c(
    "diff.high.angry.uprightVSinverted",
    "diff.high.neutral.uprightVSinverted",
    "diff.high.irregular.uprightVSinverted",
    "diff.low.angry.uprightVSinverted",
    "diff.low.neutral.uprightVSinverted",
    "diff.low.irregular.uprightVSinverted"
  )
) %>%
  droplevels()

par(mfrow = c(2, 3))

for (i in 1:length(levels(pilot2.posterior.test.orientation$condition))) {
  temp.data <- filter(pilot2.posterior.test.orientation, condition == levels(condition)[i])

  plotPost(
    pull(temp.data, CS),
    credMass = 0.95,
    compVal = 0,
    ROPE = NULL,
    xlab = "",
    col = "#b3cde0",
    showCurve = FALSE,
    cex = 1,
    main = levels(temp.data$condition)[i]
  )
}

### regularity
pilot2.posterior.test.regularity <- filter(
  pilot2.posterior.test,
  condition == c(
    "diff.high.upright.angryVSneutral",
    "diff.high.upright.angryVSirregular",
    "diff.high.upright.neutralVSirregular",
    "diff.low.upright.angryVSneutral",
    "diff.low.upright.angryVSirregular",
    "diff.low.upright.neutralVSirregular",
    "diff.high.inverted.angryVSneutral",
    "diff.high.inverted.angryVSirregular",
    "diff.high.inverted.neutralVSirregular",
    "diff.low.inverted.angryVSneutral",
    "diff.low.inverted.angryVSirregular",
    "diff.low.inverted.neutralVSirregular"
  )
) %>%
  droplevels()

par(mfrow = c(4, 3))

for (i in 1:length(levels(pilot2.posterior.test.regularity$condition))) {
  temp.data <- filter(pilot2.posterior.test.regularity, condition == levels(condition)[i])

  plotPost(
    pull(temp.data, CS),
    credMass = 0.95,
    compVal = 0,
    ROPE = NULL,
    xlab = "",
    col = "#b3cde0",
    showCurve = FALSE,
    cex = 1,
    main = levels(temp.data$condition)[i]
  )
}

### variability
pilot2.posterior.test.variability <- filter(
  pilot2.posterior.test,
  condition == c(
    "diff.upright.angry.highVSlow",
    "diff.upright.neutral.highVSlow",
    "diff.upright.irregular.highVSlow",
    "diff.inverted.angry.highVSlow",
    "diff.inverted.neutral.highVSlow",
    "diff.inverted.irregular.highVSlow"
  )
) %>%
  droplevels()

par(mfrow = c(2, 3))

for (i in 1:length(levels(pilot2.posterior.test.variability$condition))) {
  temp.data <- filter(pilot2.posterior.test.variability, condition == levels(condition)[i])

  plotPost(
    pull(temp.data, CS),
    credMass = 0.95,
    compVal = 0,
    ROPE = NULL,
    xlab = "",
    col = "#b3cde0",
    showCurve = FALSE,
    cex = 1,
    main = levels(temp.data$condition)[i]
  )
}

Take-home messages:

• comparison with 0
  • upright angry and neutral faces elicit SSR larger than noise, in all orientations and within-identity emotion variabilities
  • upright irregular faces elicit SSR not distinguishable from noise, in both within-identity emotion variabilities
  • inverted irregular faces elicit SSR slightly larger than noise only when within-identity emotion variability is high
• paired comparisons:
  • orientation
    • upright and inverted faces elicit similar SSR in all regularities and within-identity emotion variabilities
    • only exception: irregular faces elicit slightly larger SSR when inverted compared to upright only when within-identity emotion variability is high
  • regularity
    • angry and neutral faces elicit larger SSR than irregular faces, in all orientations and within-identity emotion variabilities
    • neutral faces elicit larger SSR than angry faces only when inverted and within-identity emotion variability is high
  • within-identity emotion variability
    • angry faces elicit similar SSR in high and low variability, in both orientations
    • neutral faces elicit larger SSR when variability is high, in both orientations
    • irregular faces elicit larger SSR when variability is high, only when inverted

---

---

Exp 1

• flickering frequency: 6 Hz
• regularity: 2 Hz
• 2 face identities
• task: detect dots on faces

# subset data
EmoSSR.exp1 <- EmoSSR.data %>%
  filter(experiment == "exp1")

exp1.model <- brm(CS ~ 0 + condition # constant effects
+ (0 + condition | participant), # varying effects
data = EmoSSR.exp1, # subset data current experiment
family = gaussian(), # likelihood function
prior = weak.priors, # priors
sample_prior = TRUE, # draw samples from the prior distribution
inits = "random", # initial parameter values in the chains
control = list(
  adapt_delta = .99, # parameters of NUTS sampler
  max_treedepth = 15
),
chains = num.chains, # number of chains
iter = num.iter, # number of iterations
warmup = num.warmup, # number of warm-up samples
thin = num.thin, # thinning rate
algorithm = "sampling", # type of sampling algorithm
cores = num.chains, # number of processor cores to use when running chains in parallel
seed = seed.smorfia # RNG seed
)

saveRDS(exp1.model, file = "exp1_model.rds", compress = "gzip") # save results

# subset data
EmoSSR.exp1 <- EmoSSR.data %>%
  filter(experiment == "exp1")

# load model
exp1.model <- readRDS("exp1_model.rds")

# summary posterior distributions & diagnostics
summary.exp1.model <-
  describe_posterior(exp1.model,
    centrality = "mean",
    ci = 0.95,
    ci_method = "hdi",
    test = NULL,
    diagnostic = "all"
  ) %>%
  mutate(
    Parameter = gsub("b_condition", "", Parameter),
    Parameter2 = gsub("_", " ", Parameter),
    condition = factor(Parameter2,
      levels =
        c(
          "upright angry high", "upright neutral high", "upright irregular high",
          "upright angry low", "upright neutral low", "upright irregular low",
          "inverted angry high", "inverted neutral high", "inverted irregular high",
          "inverted angry low", "inverted neutral low", "inverted irregular low"
        )
    )
  ) %>%
  dplyr::select(Parameter, Mean, HDI95_Low = CI_low, HDI95_High = CI_high, Estimated_Sample_Size = ESS, MonteCarlo_StdErr = MCSE)

kable(summary.exp1.model, digits = 2)

Parameter	Mean	HDI95_Low	HDI95_High	Estimated_Sample_Size	MonteCarlo_StdErr
inverted_angry_high	0.02	0.01	0.03	9620	0
inverted_angry_low	0.01	0.00	0.02	13004	0
inverted_irregular_high	0.00	-0.01	0.00	11684	0
inverted_irregular_high	0.00	-0.01	0.00	11684	0
inverted_irregular_low	0.00	-0.01	0.00	12484	0
inverted_irregular_low	0.00	-0.01	0.00	12484	0
inverted_neutral_high	0.04	0.02	0.05	10695	0
inverted_neutral_low	0.02	0.01	0.03	11560	0
upright_angry_high	0.03	0.02	0.04	13275	0
upright_angry_low	0.02	0.01	0.03	13111	0
upright_irregular_high	0.00	-0.01	0.01	13757	0
upright_irregular_high	0.00	-0.01	0.01	13757	0
upright_irregular_low	0.00	-0.01	0.01	13403	0
upright_irregular_low	0.00	-0.01	0.01	13403	0
upright_neutral_high	0.05	0.03	0.07	12948	0
upright_neutral_low	0.03	0.01	0.04	12477	0

# MCMC chains
exp1.model %>%
  spread_draws(`b_.*`, regex = TRUE) %>%
  dplyr::select(
    "Chain" = ".chain",
    "upright angry high" = "b_conditionupright_angry_high",
    "upright neutral high" = "b_conditionupright_neutral_high",
    "upright irregular high" = "b_conditionupright_irregular_high",
    "upright angry low" = "b_conditionupright_angry_low",
    "upright neutral low" = "b_conditionupright_neutral_low",
    "upright irregular low" = "b_conditionupright_irregular_low",
    "inverted angry high" = "b_conditioninverted_angry_high",
    "inverted neutral high" = "b_conditioninverted_neutral_high",
    "inverted irregular high" = "b_conditioninverted_irregular_high",
    "inverted angry low" = "b_conditioninverted_angry_low",
    "inverted neutral low" = "b_conditioninverted_neutral_low",
    "inverted irregular low" = "b_conditioninverted_irregular_low"
  ) %>%
  as.data.frame() %>%
  mcmc_trace(facet_args = list(ncol = 3)) +
  geom_vline(
    xintercept = seq(0, 2000, 500),
    linetype = "dotted",
    colour = "#999999",
    size = .8,
    alpha = .5
  ) +
  ggtitle("chain convergence") +
  theme_EmoSSR +
  theme(legend.position = "none")

# posterior predictive checks
exp1.model %>%
  posterior_predict(draws = 500) %>%
  ppc_stat_grouped(
    y = pull(EmoSSR.exp1, CS),
    group = pull(EmoSSR.exp1, condition),
    stat = "mean"
  ) +
  ggtitle("posterior predictive checks") +
  theme_EmoSSR +
  theme(legend.position = "none")

exp1.posterior.test <- exp1.model %>%
  spread_draws(`b_.*`, regex = TRUE) %>%
  dplyr::select(
    "upright angry high" = "b_conditionupright_angry_high",
    "upright neutral high" = "b_conditionupright_neutral_high",
    "upright irregular high" = "b_conditionupright_irregular_high",
    "upright angry low" = "b_conditionupright_angry_low",
    "upright neutral low" = "b_conditionupright_neutral_low",
    "upright irregular low" = "b_conditionupright_irregular_low",
    "inverted angry high" = "b_conditioninverted_angry_high",
    "inverted neutral high" = "b_conditioninverted_neutral_high",
    "inverted irregular high" = "b_conditioninverted_irregular_high",
    "inverted angry low" = "b_conditioninverted_angry_low",
    "inverted neutral low" = "b_conditioninverted_neutral_low",
    "inverted irregular low" = "b_conditioninverted_irregular_low"
  ) %>%
  mutate(
    ### orientation
    # angry high
    diff.high.angry.uprightVSinverted = `upright angry high` - `inverted angry high`,
    # neutral high
    diff.high.neutral.uprightVSinverted = `upright neutral high` - `inverted neutral high`,
    # irregular high
    diff.high.irregular.uprightVSinverted = `upright irregular high` - `inverted irregular high`,
    # angry low
    diff.low.angry.uprightVSinverted = `upright angry low` - `inverted angry low`,
    # neutral high
    diff.low.neutral.uprightVSinverted = `upright neutral low` - `inverted neutral low`,
    # irregular high
    diff.low.irregular.uprightVSinverted = `upright irregular low` - `inverted irregular low`,
    ### regularity
    ## upright high
    # angry minus neutral
    diff.high.upright.angryVSneutral = `upright angry high` - `upright neutral high`,
    # angry minus irregular
    diff.high.upright.angryVSirregular = `upright angry high` - `upright irregular high`,
    # neutral minus irregular
    diff.high.upright.neutralVSirregular = `upright neutral high` - `upright irregular high`,
    ## upright low
    # angry minus neutral
    diff.low.upright.angryVSneutral = `upright angry low` - `upright neutral low`,
    # angry minus irregular
    diff.low.upright.angryVSirregular = `upright angry low` - `upright irregular low`,
    # neutral minus irregular
    diff.low.upright.neutralVSirregular = `upright neutral low` - `upright irregular low`,
    ## inverted high
    # angry minus neutral
    diff.high.inverted.angryVSneutral = `inverted angry high` - `inverted neutral high`,
    # angry minus irregular
    diff.high.inverted.angryVSirregular = `inverted angry high` - `inverted irregular high`,
    # neutral minus irregular
    diff.high.inverted.neutralVSirregular = `inverted neutral high` - `inverted irregular high`,
    ## inverted low
    # angry minus neutral
    diff.low.inverted.angryVSneutral = `inverted angry low` - `inverted neutral low`,
    # angry minus irregular
    diff.low.inverted.angryVSirregular = `inverted angry low` - `inverted irregular low`,
    # neutral minus irregular
    diff.low.inverted.neutralVSirregular = `inverted neutral low` - `inverted irregular low`,
    ### variability
    ## upright angry
    diff.upright.angry.highVSlow = `upright angry high` - `upright angry low`,
    ## upright neutral
    diff.upright.neutral.highVSlow = `upright neutral high` - `upright neutral low`,
    ## upright irregular
    diff.upright.irregular.highVSlow = `upright irregular high` - `upright irregular low`,
    ## inverted angry
    diff.inverted.angry.highVSlow = `inverted angry high` - `inverted angry low`,
    ## inverted neutral
    diff.inverted.neutral.highVSlow = `inverted neutral high` - `inverted neutral low`,
    ## inverted irregular
    diff.inverted.irregular.highVSlow = `inverted irregular high` - `inverted irregular low`
  ) %>%
  gather(key = "condition", value = "CS") %>%
  mutate(condition = factor(condition,
    levels = c(
      "upright angry high", "upright neutral high", "upright irregular high",
      "upright angry low", "upright neutral low", "upright irregular low",
      "inverted angry high", "inverted neutral high", "inverted irregular high",
      "inverted angry low", "inverted neutral low", "inverted irregular low",
      "diff.high.angry.uprightVSinverted",
      "diff.high.neutral.uprightVSinverted",
      "diff.high.irregular.uprightVSinverted",
      "diff.low.angry.uprightVSinverted",
      "diff.low.neutral.uprightVSinverted",
      "diff.low.irregular.uprightVSinverted",
      "diff.high.upright.angryVSneutral",
      "diff.high.upright.angryVSirregular",
      "diff.high.upright.neutralVSirregular",
      "diff.low.upright.angryVSneutral",
      "diff.low.upright.angryVSirregular",
      "diff.low.upright.neutralVSirregular",
      "diff.high.inverted.angryVSneutral",
      "diff.high.inverted.angryVSirregular",
      "diff.high.inverted.neutralVSirregular",
      "diff.low.inverted.angryVSneutral",
      "diff.low.inverted.angryVSirregular",
      "diff.low.inverted.neutralVSirregular",
      "diff.upright.angry.highVSlow",
      "diff.upright.neutral.highVSlow",
      "diff.upright.irregular.highVSlow",
      "diff.inverted.angry.highVSlow",
      "diff.inverted.neutral.highVSlow",
      "diff.inverted.irregular.highVSlow"
    )
  ))

# summary
summary.exp1.posterior.test <- exp1.posterior.test %>%
  group_by(condition) %>%
  dplyr::summarize(
    mean = mean(CS),
    hdi.95.low = hdi(CS)[1],
    hdi.95.high = hdi(CS)[2],
    evidence.ratio = ifelse(mean < 0,
      length(which(CS < 0)) / length(which(CS > 0)),
      length(which(CS > 0)) / length(which(CS < 0))
    )
  ) %>%
  ungroup()

kable(summary.exp1.posterior.test, digits = 2)

condition	mean	hdi.95.low	hdi.95.high	evidence.ratio
upright angry high	0.03	0.02	0.04	Inf
upright neutral high	0.05	0.03	0.07	15999.00
upright irregular high	0.00	-0.01	0.01	1.96
upright angry low	0.02	0.01	0.03	2665.67
upright neutral low	0.03	0.01	0.04	3999.00
upright irregular low	0.00	-0.01	0.01	1.06
inverted angry high	0.02	0.01	0.03	Inf
inverted neutral high	0.04	0.02	0.05	Inf
inverted irregular high	0.00	-0.01	0.00	10.49
inverted angry low	0.01	0.00	0.02	799.00
inverted neutral low	0.02	0.01	0.03	Inf
inverted irregular low	0.00	-0.01	0.00	2.44
diff.high.angry.uprightVSinverted	0.01	0.00	0.02	17.16
diff.high.neutral.uprightVSinverted	0.01	-0.01	0.03	7.62
diff.high.irregular.uprightVSinverted	0.00	0.00	0.01	7.57
diff.low.angry.uprightVSinverted	0.01	0.00	0.02	10.15
diff.low.neutral.uprightVSinverted	0.01	-0.01	0.02	2.63
diff.low.irregular.uprightVSinverted	0.00	-0.01	0.01	1.90
diff.high.upright.angryVSneutral	-0.02	-0.04	0.01	10.83
diff.high.upright.angryVSirregular	0.03	0.02	0.04	Inf
diff.high.upright.neutralVSirregular	0.05	0.03	0.07	15999.00
diff.low.upright.angryVSneutral	-0.01	-0.02	0.01	6.57
diff.low.upright.angryVSirregular	0.02	0.01	0.03	245.15
diff.low.upright.neutralVSirregular	0.03	0.01	0.05	1141.86
diff.high.inverted.angryVSneutral	-0.01	-0.03	0.00	16.72
diff.high.inverted.angryVSirregular	0.03	0.02	0.04	Inf
diff.high.inverted.neutralVSirregular	0.04	0.03	0.05	Inf
diff.low.inverted.angryVSneutral	-0.01	-0.02	0.00	102.90
diff.low.inverted.angryVSirregular	0.01	0.00	0.02	409.26
diff.low.inverted.neutralVSirregular	0.03	0.01	0.04	Inf
diff.upright.angry.highVSlow	0.01	0.00	0.03	30.37
diff.upright.neutral.highVSlow	0.02	0.00	0.04	39.51
diff.upright.irregular.highVSlow	0.00	-0.01	0.01	1.56
diff.inverted.angry.highVSlow	0.01	0.00	0.02	49.63
diff.inverted.neutral.highVSlow	0.01	0.00	0.03	23.46
diff.inverted.irregular.highVSlow	0.00	-0.01	0.01	1.88

### CSs higher than noise? ###
exp1.posterior.test.VS.0 <- filter(
  exp1.posterior.test,
  condition == c(
    "upright angry high", "upright neutral high", "upright irregular high",
    "upright angry low", "upright neutral low", "upright irregular low",
    "inverted angry high", "inverted neutral high", "inverted irregular high",
    "inverted angry low", "inverted neutral low", "inverted irregular low"
  )
) %>%
  droplevels()

par(mfrow = c(2, 3))

for (i in 1:length(levels(exp1.posterior.test.VS.0$condition))) {
  temp.data <- filter(exp1.posterior.test.VS.0, condition == levels(condition)[i])

  plotPost(
    pull(temp.data, CS),
    credMass = 0.95,
    compVal = 0,
    ROPE = NULL,
    xlab = "",
    col = "#b3cde0",
    showCurve = FALSE,
    cex = 1,
    main = levels(temp.data$condition)[i]
  )
}

### Paired comparisons ###

### orientation
exp1.posterior.test.orientation <- filter(
  exp1.posterior.test,
  condition == c(
    "diff.high.angry.uprightVSinverted",
    "diff.high.neutral.uprightVSinverted",
    "diff.high.irregular.uprightVSinverted",
    "diff.low.angry.uprightVSinverted",
    "diff.low.neutral.uprightVSinverted",
    "diff.low.irregular.uprightVSinverted"
  )
) %>%
  droplevels()

par(mfrow = c(2, 3))

for (i in 1:length(levels(exp1.posterior.test.orientation$condition))) {
  temp.data <- filter(exp1.posterior.test.orientation, condition == levels(condition)[i])

  plotPost(
    pull(temp.data, CS),
    credMass = 0.95,
    compVal = 0,
    ROPE = NULL,
    xlab = "",
    col = "#b3cde0",
    showCurve = FALSE,
    cex = 1,
    main = levels(temp.data$condition)[i]
  )
}

### regularity
exp1.posterior.test.regularity <- filter(
  exp1.posterior.test,
  condition == c(
    "diff.high.upright.angryVSneutral",
    "diff.high.upright.angryVSirregular",
    "diff.high.upright.neutralVSirregular",
    "diff.low.upright.angryVSneutral",
    "diff.low.upright.angryVSirregular",
    "diff.low.upright.neutralVSirregular",
    "diff.high.inverted.angryVSneutral",
    "diff.high.inverted.angryVSirregular",
    "diff.high.inverted.neutralVSirregular",
    "diff.low.inverted.angryVSneutral",
    "diff.low.inverted.angryVSirregular",
    "diff.low.inverted.neutralVSirregular"
  )
) %>%
  droplevels()

par(mfrow = c(4, 3))

for (i in 1:length(levels(exp1.posterior.test.regularity$condition))) {
  temp.data <- filter(exp1.posterior.test.regularity, condition == levels(condition)[i])

  plotPost(
    pull(temp.data, CS),
    credMass = 0.95,
    compVal = 0,
    ROPE = NULL,
    xlab = "",
    col = "#b3cde0",
    showCurve = FALSE,
    cex = 1,
    main = levels(temp.data$condition)[i]
  )
}

### variability
exp1.posterior.test.variability <- filter(
  exp1.posterior.test,
  condition == c(
    "diff.upright.angry.highVSlow",
    "diff.upright.neutral.highVSlow",
    "diff.upright.irregular.highVSlow",
    "diff.inverted.angry.highVSlow",
    "diff.inverted.neutral.highVSlow",
    "diff.inverted.irregular.highVSlow"
  )
) %>%
  droplevels()

par(mfrow = c(2, 3))

for (i in 1:length(levels(exp1.posterior.test.variability$condition))) {
  temp.data <- filter(exp1.posterior.test.variability, condition == levels(condition)[i])

  plotPost(
    pull(temp.data, CS),
    credMass = 0.95,
    compVal = 0,
    ROPE = NULL,
    xlab = "",
    col = "#b3cde0",
    showCurve = FALSE,
    cex = 1,
    main = levels(temp.data$condition)[i]
  )
}

Take-home messages:

• comparison with 0
  • upright angry and neutral faces elicit SSR larger than noise, in all orientations and within-identity emotion variabilities
  • irregular faces elicit SSR not distinguishable from noise, in all orientations and within-identity emotion variabilities
• paired comparisons:
  • orientation
    • upright and inverted faces elicit similar SSR in all regularities and within-identity emotion variabilities
  • regularity
    • angry and neutral faces elicit larger SSR than irregular faces, in all orientations and within-identity emotion variabilities
    • neutral faces elicit larger SSR than angry faces only when inverted and within-identity emotion variability is low
  • within-identity emotion variability
    • angry faces elicit larger SSR when within-identity emotion variability is high, in both orientations
    • neutral faces elicit larger SSR when variability is high, in both orientations
    • irregular faces elicit similar SSR in high and low variability, in both orientations

---

---

Exp 2

• flickering frequency: 6 Hz
• regularity: 2 Hz
• 2 face identities
• task: passive viewing

# subset data
EmoSSR.exp2 <- EmoSSR.data %>%
  filter(experiment == "exp2")

exp2.model <- brm(CS ~ 0 + condition # constant effects
+ (0 + condition | participant), # varying effects
data = EmoSSR.exp2, # subset data current experiment
family = gaussian(), # likelihood function
prior = weak.priors, # priors
sample_prior = TRUE, # draw samples from the prior distribution
inits = "random", # initial parameter values in the chains
control = list(
  adapt_delta = .99, # parameters of NUTS sampler
  max_treedepth = 15
),
chains = num.chains, # number of chains
iter = num.iter, # number of iterations
warmup = num.warmup, # number of warm-up samples
thin = num.thin, # thinning rate
algorithm = "sampling", # type of sampling algorithm
cores = num.chains, # number of processor cores to use when running chains in parallel
seed = seed.smorfia # RNG seed
)

saveRDS(exp2.model, file = "exp2_model.rds", compress = "gzip") # save results

# subset data
EmoSSR.exp2 <- EmoSSR.data %>%
  filter(experiment == "exp2")

# load model
exp2.model <- readRDS("exp2_model.rds")

# summary posterior distributions & diagnostics
summary.exp2.model <-
  describe_posterior(exp2.model,
    centrality = "mean",
    ci = 0.95,
    ci_method = "hdi",
    test = NULL,
    diagnostic = "all"
  ) %>%
  mutate(
    Parameter = gsub("b_condition", "", Parameter),
    Parameter2 = gsub("_", " ", Parameter),
    condition = factor(Parameter2,
      levels =
        c(
          "upright angry high", "upright neutral high", "upright irregular high",
          "upright angry low", "upright neutral low", "upright irregular low",
          "inverted angry high", "inverted neutral high", "inverted irregular high",
          "inverted angry low", "inverted neutral low", "inverted irregular low"
        )
    )
  ) %>%
  dplyr::select(Parameter, Mean, HDI95_Low = CI_low, HDI95_High = CI_high, Estimated_Sample_Size = ESS, MonteCarlo_StdErr = MCSE)

kable(summary.exp2.model, digits = 2)

Parameter	Mean	HDI95_Low	HDI95_High	Estimated_Sample_Size	MonteCarlo_StdErr
inverted_angry_high	0.03	0.02	0.04	6558	0
inverted_angry_low	0.01	0.00	0.02	10806	0
inverted_irregular_high	0.00	0.00	0.01	12659	0
inverted_irregular_high	0.00	0.00	0.01	12659	0
inverted_irregular_low	0.00	-0.01	0.00	12463	0
inverted_irregular_low	0.00	-0.01	0.00	12463	0
inverted_neutral_high	0.05	0.03	0.06	10526	0
inverted_neutral_low	0.01	0.01	0.02	13144	0
upright_angry_high	0.03	0.02	0.05	10554	0
upright_angry_low	0.02	0.00	0.03	11366	0
upright_irregular_high	0.00	-0.01	0.00	12514	0
upright_irregular_high	0.00	-0.01	0.00	12514	0
upright_irregular_low	0.01	0.00	0.02	12340	0
upright_irregular_low	0.01	0.00	0.02	12340	0
upright_neutral_high	0.06	0.04	0.08	13483	0
upright_neutral_low	0.02	0.02	0.03	13070	0

# MCMC chains
exp2.model %>%
  spread_draws(`b_.*`, regex = TRUE) %>%
  dplyr::select(
    "Chain" = ".chain",
    "upright angry high" = "b_conditionupright_angry_high",
    "upright neutral high" = "b_conditionupright_neutral_high",
    "upright irregular high" = "b_conditionupright_irregular_high",
    "upright angry low" = "b_conditionupright_angry_low",
    "upright neutral low" = "b_conditionupright_neutral_low",
    "upright irregular low" = "b_conditionupright_irregular_low",
    "inverted angry high" = "b_conditioninverted_angry_high",
    "inverted neutral high" = "b_conditioninverted_neutral_high",
    "inverted irregular high" = "b_conditioninverted_irregular_high",
    "inverted angry low" = "b_conditioninverted_angry_low",
    "inverted neutral low" = "b_conditioninverted_neutral_low",
    "inverted irregular low" = "b_conditioninverted_irregular_low"
  ) %>%
  as.data.frame() %>%
  mcmc_trace(facet_args = list(ncol = 3)) +
  geom_vline(
    xintercept = seq(0, 2000, 500),
    linetype = "dotted",
    colour = "#999999",
    size = .8,
    alpha = .5
  ) +
  ggtitle("chain convergence") +
  theme_EmoSSR +
  theme(legend.position = "none")

# posterior predictive checks
exp2.model %>%
  posterior_predict(draws = 500) %>%
  ppc_stat_grouped(
    y = pull(EmoSSR.exp2, CS),
    group = pull(EmoSSR.exp2, condition),
    stat = "mean"
  ) +
  ggtitle("posterior predictive checks") +
  theme_EmoSSR +
  theme(legend.position = "none")

exp2.posterior.test <- exp2.model %>%
  spread_draws(`b_.*`, regex = TRUE) %>%
  dplyr::select(
    "upright angry high" = "b_conditionupright_angry_high",
    "upright neutral high" = "b_conditionupright_neutral_high",
    "upright irregular high" = "b_conditionupright_irregular_high",
    "upright angry low" = "b_conditionupright_angry_low",
    "upright neutral low" = "b_conditionupright_neutral_low",
    "upright irregular low" = "b_conditionupright_irregular_low",
    "inverted angry high" = "b_conditioninverted_angry_high",
    "inverted neutral high" = "b_conditioninverted_neutral_high",
    "inverted irregular high" = "b_conditioninverted_irregular_high",
    "inverted angry low" = "b_conditioninverted_angry_low",
    "inverted neutral low" = "b_conditioninverted_neutral_low",
    "inverted irregular low" = "b_conditioninverted_irregular_low"
  ) %>%
  mutate(
    ### orientation
    # angry high
    diff.high.angry.uprightVSinverted = `upright angry high` - `inverted angry high`,
    # neutral high
    diff.high.neutral.uprightVSinverted = `upright neutral high` - `inverted neutral high`,
    # irregular high
    diff.high.irregular.uprightVSinverted = `upright irregular high` - `inverted irregular high`,
    # angry low
    diff.low.angry.uprightVSinverted = `upright angry low` - `inverted angry low`,
    # neutral high
    diff.low.neutral.uprightVSinverted = `upright neutral low` - `inverted neutral low`,
    # irregular high
    diff.low.irregular.uprightVSinverted = `upright irregular low` - `inverted irregular low`,
    ### regularity
    ## upright high
    # angry minus neutral
    diff.high.upright.angryVSneutral = `upright angry high` - `upright neutral high`,
    # angry minus irregular
    diff.high.upright.angryVSirregular = `upright angry high` - `upright irregular high`,
    # neutral minus irregular
    diff.high.upright.neutralVSirregular = `upright neutral high` - `upright irregular high`,
    ## upright low
    # angry minus neutral
    diff.low.upright.angryVSneutral = `upright angry low` - `upright neutral low`,
    # angry minus irregular
    diff.low.upright.angryVSirregular = `upright angry low` - `upright irregular low`,
    # neutral minus irregular
    diff.low.upright.neutralVSirregular = `upright neutral low` - `upright irregular low`,
    ## inverted high
    # angry minus neutral
    diff.high.inverted.angryVSneutral = `inverted angry high` - `inverted neutral high`,
    # angry minus irregular
    diff.high.inverted.angryVSirregular = `inverted angry high` - `inverted irregular high`,
    # neutral minus irregular
    diff.high.inverted.neutralVSirregular = `inverted neutral high` - `inverted irregular high`,
    ## inverted low
    # angry minus neutral
    diff.low.inverted.angryVSneutral = `inverted angry low` - `inverted neutral low`,
    # angry minus irregular
    diff.low.inverted.angryVSirregular = `inverted angry low` - `inverted irregular low`,
    # neutral minus irregular
    diff.low.inverted.neutralVSirregular = `inverted neutral low` - `inverted irregular low`,
    ### variability
    ## upright angry
    diff.upright.angry.highVSlow = `upright angry high` - `upright angry low`,
    ## upright neutral
    diff.upright.neutral.highVSlow = `upright neutral high` - `upright neutral low`,
    ## upright irregular
    diff.upright.irregular.highVSlow = `upright irregular high` - `upright irregular low`,
    ## inverted angry
    diff.inverted.angry.highVSlow = `inverted angry high` - `inverted angry low`,
    ## inverted neutral
    diff.inverted.neutral.highVSlow = `inverted neutral high` - `inverted neutral low`,
    ## inverted irregular
    diff.inverted.irregular.highVSlow = `inverted irregular high` - `inverted irregular low`
  ) %>%
  gather(key = "condition", value = "CS") %>%
  mutate(condition = factor(condition,
    levels = c(
      "upright angry high", "upright neutral high", "upright irregular high",
      "upright angry low", "upright neutral low", "upright irregular low",
      "inverted angry high", "inverted neutral high", "inverted irregular high",
      "inverted angry low", "inverted neutral low", "inverted irregular low",
      "diff.high.angry.uprightVSinverted",
      "diff.high.neutral.uprightVSinverted",
      "diff.high.irregular.uprightVSinverted",
      "diff.low.angry.uprightVSinverted",
      "diff.low.neutral.uprightVSinverted",
      "diff.low.irregular.uprightVSinverted",
      "diff.high.upright.angryVSneutral",
      "diff.high.upright.angryVSirregular",
      "diff.high.upright.neutralVSirregular",
      "diff.low.upright.angryVSneutral",
      "diff.low.upright.angryVSirregular",
      "diff.low.upright.neutralVSirregular",
      "diff.high.inverted.angryVSneutral",
      "diff.high.inverted.angryVSirregular",
      "diff.high.inverted.neutralVSirregular",
      "diff.low.inverted.angryVSneutral",
      "diff.low.inverted.angryVSirregular",
      "diff.low.inverted.neutralVSirregular",
      "diff.upright.angry.highVSlow",
      "diff.upright.neutral.highVSlow",
      "diff.upright.irregular.highVSlow",
      "diff.inverted.angry.highVSlow",
      "diff.inverted.neutral.highVSlow",
      "diff.inverted.irregular.highVSlow"
    )
  ))

# summary
summary.exp2.posterior.test <- exp2.posterior.test %>%
  group_by(condition) %>%
  dplyr::summarize(
    mean = mean(CS),
    hdi.95.low = hdi(CS)[1],
    hdi.95.high = hdi(CS)[2],
    evidence.ratio = ifelse(mean < 0,
      length(which(CS < 0)) / length(which(CS > 0)),
      length(which(CS > 0)) / length(which(CS < 0))
    )
  ) %>%
  ungroup()

kable(summary.exp2.posterior.test, digits = 2)

condition	mean	hdi.95.low	hdi.95.high	evidence.ratio
upright angry high	0.03	0.02	0.05	Inf
upright neutral high	0.06	0.04	0.08	Inf
upright irregular high	0.00	-0.01	0.00	7.62
upright angry low	0.02	0.00	0.03	257.06
upright neutral low	0.02	0.02	0.03	Inf
upright irregular low	0.01	0.00	0.02	44.58
inverted angry high	0.03	0.02	0.04	Inf
inverted neutral high	0.05	0.03	0.06	Inf
inverted irregular high	0.00	0.00	0.01	7.26
inverted angry low	0.01	0.00	0.02	591.59
inverted neutral low	0.01	0.01	0.02	1999.00
inverted irregular low	0.00	-0.01	0.00	4.63
diff.high.angry.uprightVSinverted	0.00	-0.01	0.02	1.66
diff.high.neutral.uprightVSinverted	0.01	-0.01	0.03	11.44
diff.high.irregular.uprightVSinverted	-0.01	-0.01	0.00	18.39
diff.low.angry.uprightVSinverted	0.00	-0.01	0.02	1.89
diff.low.neutral.uprightVSinverted	0.01	0.00	0.02	75.56
diff.low.irregular.uprightVSinverted	0.01	0.00	0.02	59.61
diff.high.upright.angryVSneutral	-0.03	-0.05	-0.01	107.11
diff.high.upright.angryVSirregular	0.04	0.02	0.05	Inf
diff.high.upright.neutralVSirregular	0.06	0.05	0.08	Inf
diff.low.upright.angryVSneutral	-0.01	-0.02	0.00	9.51
diff.low.upright.angryVSirregular	0.01	-0.01	0.02	3.35
diff.low.upright.neutralVSirregular	0.02	0.00	0.03	189.48
diff.high.inverted.angryVSneutral	-0.01	-0.03	0.00	17.14
diff.high.inverted.angryVSirregular	0.03	0.01	0.04	15999.00
diff.high.inverted.neutralVSirregular	0.04	0.03	0.06	Inf
diff.low.inverted.angryVSneutral	0.00	-0.01	0.01	1.03
diff.low.inverted.angryVSirregular	0.01	0.01	0.02	940.18
diff.low.inverted.neutralVSirregular	0.01	0.01	0.02	2284.71
diff.upright.angry.highVSlow	0.02	0.00	0.04	42.24
diff.upright.neutral.highVSlow	0.04	0.02	0.05	2284.71
diff.upright.irregular.highVSlow	-0.01	-0.02	0.00	94.24
diff.inverted.angry.highVSlow	0.02	0.01	0.03	362.64
diff.inverted.neutral.highVSlow	0.03	0.02	0.05	3199.00
diff.inverted.irregular.highVSlow	0.00	0.00	0.01	12.75

### CSs higher than noise? ###
exp2.posterior.test.VS.0 <- filter(
  exp2.posterior.test,
  condition == c(
    "upright angry high", "upright neutral high", "upright irregular high",
    "upright angry low", "upright neutral low", "upright irregular low",
    "inverted angry high", "inverted neutral high", "inverted irregular high",
    "inverted angry low", "inverted neutral low", "inverted irregular low"
  )
) %>%
  droplevels()

par(mfrow = c(2, 3))

for (i in 1:length(levels(exp2.posterior.test.VS.0$condition))) {
  temp.data <- filter(exp2.posterior.test.VS.0, condition == levels(condition)[i])

  plotPost(
    pull(temp.data, CS),
    credMass = 0.95,
    compVal = 0,
    ROPE = NULL,
    xlab = "",
    col = "#b3cde0",
    showCurve = FALSE,
    cex = 1,
    main = levels(temp.data$condition)[i]
  )
}

### Paired comparisons ###

### orientation
exp2.posterior.test.orientation <- filter(
  exp2.posterior.test,
  condition == c(
    "diff.high.angry.uprightVSinverted",
    "diff.high.neutral.uprightVSinverted",
    "diff.high.irregular.uprightVSinverted",
    "diff.low.angry.uprightVSinverted",
    "diff.low.neutral.uprightVSinverted",
    "diff.low.irregular.uprightVSinverted"
  )
) %>%
  droplevels()

par(mfrow = c(2, 3))

for (i in 1:length(levels(exp2.posterior.test.orientation$condition))) {
  temp.data <- filter(exp2.posterior.test.orientation, condition == levels(condition)[i])

  plotPost(
    pull(temp.data, CS),
    credMass = 0.95,
    compVal = 0,
    ROPE = NULL,
    xlab = "",
    col = "#b3cde0",
    showCurve = FALSE,
    cex = 1,
    main = levels(temp.data$condition)[i]
  )
}

### regularity
exp2.posterior.test.regularity <- filter(
  exp2.posterior.test,
  condition == c(
    "diff.high.upright.angryVSneutral",
    "diff.high.upright.angryVSirregular",
    "diff.high.upright.neutralVSirregular",
    "diff.low.upright.angryVSneutral",
    "diff.low.upright.angryVSirregular",
    "diff.low.upright.neutralVSirregular",
    "diff.high.inverted.angryVSneutral",
    "diff.high.inverted.angryVSirregular",
    "diff.high.inverted.neutralVSirregular",
    "diff.low.inverted.angryVSneutral",
    "diff.low.inverted.angryVSirregular",
    "diff.low.inverted.neutralVSirregular"
  )
) %>%
  droplevels()

par(mfrow = c(4, 3))

for (i in 1:length(levels(exp2.posterior.test.regularity$condition))) {
  temp.data <- filter(exp2.posterior.test.regularity, condition == levels(condition)[i])

  plotPost(
    pull(temp.data, CS),
    credMass = 0.95,
    compVal = 0,
    ROPE = NULL,
    xlab = "",
    col = "#b3cde0",
    showCurve = FALSE,
    cex = 1,
    main = levels(temp.data$condition)[i]
  )
}

### variability
exp2.posterior.test.variability <- filter(
  exp2.posterior.test,
  condition == c(
    "diff.upright.angry.highVSlow",
    "diff.upright.neutral.highVSlow",
    "diff.upright.irregular.highVSlow",
    "diff.inverted.angry.highVSlow",
    "diff.inverted.neutral.highVSlow",
    "diff.inverted.irregular.highVSlow"
  )
) %>%
  droplevels()

par(mfrow = c(2, 3))

for (i in 1:length(levels(exp2.posterior.test.variability$condition))) {
  temp.data <- filter(exp2.posterior.test.variability, condition == levels(condition)[i])

  plotPost(
    pull(temp.data, CS),
    credMass = 0.95,
    compVal = 0,
    ROPE = NULL,
    xlab = "",
    col = "#b3cde0",
    showCurve = FALSE,
    cex = 1,
    main = levels(temp.data$condition)[i]
  )
}

Take-home messages:

• comparison with 0
  • upright angry and neutral faces elicit SSR larger than noise, in all orientations and within-identity emotion variabilities
  • upright irregular faces elicit SSR slightly larger than noise only when within-identity emotion variability is low
  • all other irregular faces elicit SSR not distinguishable from noise
• paired comparisons:
  • orientation
    • upright and inverted faces elicit similar SSR in all regularities and within-identity emotion variabilities
    • neutral and irregular faces elicit slightly larger SSR when upright compared to inverted only when within-identity emotion variability is low
  • regularity
    • angry and neutral faces elicit larger SSR than irregular faces, in all orientations and within-identity emotion variabilities (exception: angry and irregular faces elicit similar SSR when upright and within-identity emotion variability is low)
    • neutral faces elicit larger SSR than angry faces only when upright and within-identity emotion variability is high
  • within-identity emotion variability
    • angry faces elicit larger SSR when within-identity emotion variability is high, in both orientations
    • neutral faces elicit larger SSR when variability is high, in both orientations
    • irregular faces elicit larger SSR in high and low variability when inverted

---

---